Functional Data Analysis (FDA)

High-performance Functional Data Analysis tools implemented in Rust with R bindings.

Packages

Package	Language	Registry	Folder	Status
fdars	R	CRAN	sipemu/fdars-r
fdars-core	Rust	crates.io	`fdars-core/`

Features

Functional Data Operations: Mean, centering, derivatives, Lp norms, geometric median
Depth Measures: Fraiman-Muniz, modal, band, modified band, random projection, random Tukey, functional spatial, kernel functional spatial, modified epigraph index
Distance Metrics: Lp distances, Hausdorff, DTW, Fourier-based semimetric, horizontal shift semimetric
Basis Representations: B-splines, Fourier basis, P-splines with GCV/AIC/BIC selection
Clustering: K-means, fuzzy c-means with silhouette and Calinski-Harabasz validation
Smoothing: Nadaraya-Watson, local linear, local polynomial, k-NN
Regression: Functional PCA, PLS, ridge regression
Outlier Detection: LRT-based outlier detection with bootstrap thresholding
Seasonal Analysis: FFT, ACF, Autoperiod, CFDAutoperiod, SAZED period detection; seasonal strength metrics; amplitude modulation detection

Installation

R (fdars)

# From GitHub (requires Rust toolchain)
devtools::install_github("sipemu/fdars-r")

# From binary release (no Rust required)
# Download from GitHub Releases, then:
install.packages("path/to/fdars_x.y.z.tgz", repos = NULL, type = "mac.binary")  # macOS
install.packages("path/to/fdars_x.y.z.zip", repos = NULL, type = "win.binary")  # Windows

Rust (fdars-core)

[dependencies]
fdars-core = "0.3"

Or install from the repository:

[dependencies]
fdars-core = { git = "https://github.com/sipemu/fdars" }

Feature Flags

parallel (default): Enable rayon-based parallel processing
linalg: Enable linear algebra features (faer, ridge regression) — requires Rust 1.84+
js: Enable WASM support with JS random number generation

For WASM builds, disable default features:

[dependencies]
fdars-core = { version = "0.3", default-features = false }

Data Layout

Functional data is represented as column-major matrices stored in flat Vec<f64>:

For n observations with m evaluation points: data[i + j * n] gives observation i at point j
2D surfaces (n observations, m1 x m2 grid): stored as n x (m1*m2) matrices

Quick Start

use fdars_core::{fdata, depth, helpers};

// Create sample functional data (3 observations, 10 points each)
let n = 3;
let m = 10;
let data: Vec<f64> = (0..(n * m)).map(|i| (i as f64).sin()).collect();
let argvals: Vec<f64> = (0..m).map(|i| i as f64 / (m - 1) as f64).collect();

// Compute mean function
let mean = fdata::mean_1d(&data, n, m);

// Compute Fraiman-Muniz depth
let depths = depth::fraiman_muniz_1d(&data, &data, n, n, m, true);

Examples

The fdars-core/examples/ directory contains 14 runnable examples progressing from basic to advanced:

#	Example	Command	Topics
01	Simulation	`cargo run -p fdars-core --example simulation`	KL expansion, eigenfunctions, noise
02	Functional Operations	`cargo run -p fdars-core --example functional_operations`	Mean, centering, derivatives, norms, inner products
03	Smoothing	`cargo run -p fdars-core --example smoothing`	Nadaraya-Watson, local linear/polynomial, k-NN
04	Basis Representation	`cargo run -p fdars-core --example basis_representation`	B-splines, Fourier, P-splines, GCV/AIC/BIC
05	Depth Measures	`cargo run -p fdars-core --example depth_measures`	8 depth measures, outlier ranking
06	Distances and Metrics	`cargo run -p fdars-core --example distances_and_metrics`	Lp, Hausdorff, DTW, Fourier, h-shift
07	Clustering	`cargo run -p fdars-core --example clustering`	K-means, fuzzy c-means, silhouette, CH index
08	Regression	`cargo run -p fdars-core --example regression`	FPCA, PLS regression
09	Outlier Detection	`cargo run -p fdars-core --example outlier_detection`	LRT bootstrap, depth confirmation
10	Seasonal Analysis	`cargo run -p fdars-core --example seasonal_analysis`	FFT, ACF, Autoperiod, SAZED, peak detection
11	Detrending	`cargo run -p fdars-core --example detrending`	Linear/polynomial/LOESS, STL decomposition
12	Streaming Depth	`cargo run -p fdars-core --example streaming_depth`	Online depth, rolling windows
13	Irregular Data	`cargo run -p fdars-core --example irregular_data`	CSR storage, regularization, kernel mean
14	Complete Pipeline	`cargo run -p fdars-core --example complete_pipeline`	End-to-end: simulate → smooth → outliers → FPCA → cluster

Performance

With the parallel feature (enabled by default), computationally intensive operations use rayon for multi-core performance. The library also supports WASM targets with sequential execution.

Documentation

R Package: https://sipemu.github.io/fdars/
Rust Crate: https://docs.rs/fdars-core

License

MIT